how do you model systems described by a set of partial differential equations in simulink or labview? for instance m having the following equations describing a simple transmission line. how do you work with them say when you need response of them in real time
(∂Vs (L,t))/∂L=-R*Is (L,t)+l ∂/∂t Is (L,t)
(∂Is (L,t))/∂L=-gVs (L,t)+c ∂/∂t Vs (L,t)
Know that the question is silly. but m really stuck with this Thanks a lot
hello, if u can convert these equations in matrix form then it can be easily modeled in matlab , if u have studied control systems subject over there we do the same make state space representation of differential equations and then solve them in matlab there are also direct commands to solve state space, there is a function block in simulink of state space hope u will find something helpful. I have done system modelling but its really a long procedure converting differential equations to matrices then converting them to equivalent circuits and so on
hello, if u can convert these equations in matrix form then it can be easily modeled in matlab , if u have studied control systems subject over there we do the same make state space representation of differential equations and then solve them in matlab there are also direct commands to solve state space, there is a function block in simulink of state space hope u will find something helpful. I have done system modelling but its really a long procedure converting differential equations to matrices then converting them to equivalent circuits and so on
can you suggest me a decent book which will talk about converting diff equn. to state space matrix?? thanx a lot any way.
also see the following link. is there anything as straightforward as that for PDEs??
http://www.youtube.com/watch?v=iAvPnHkz-ww
book "control system engineering by norman nise" and "modern control engineering by k.ogata", if you specify ur problem may be i can guide u more relevant to it may be the solution is simple and u get stuck in learning state space and give me a little time i tell u another simple solution just let me cross check it first with a friend ok
actually i need to model a duct (and study the acoustic property of it) being an electrical student i simply converted the dut to its electrical equivalent ie transmission line now the equations that govorns a transmission line are those i wrote previously. it can be converted to ode and then modeled easily in simulink or labview but then the model becomes frequency dependent...and i want to give a random noise as input to the model then what is the freq??? so the only way left is to model the PDEs directly... that is why i was asking can't pdes be modeled as ODEs?
the freq is the resonant frequency which is derived from the transmission line model as u want to measure the acoustic property so definitely u will be needing resonant frequnecy
dude i need to plot the transmission loss in db vs the frequency. i can do it dy exiting the duct seperately with pure tone at different freq. but that takes a lot of manual effort change the feq take the sound then plot........ my idea is to exite the tube with white noice and take fft of the output which should give me the thing in one go.
From the two equations we can find the wave equation. We then find that the propagation constant is the square root of (R+j(omega)L)*(G+j(omega)C)). If the propation constant is represented by gamma then the wave goes as exp(-(gamma)x). Now to get the loss you take the real part of this expression and convert it to dB. Then you can run a simple program to calculate dB vs. omega.
To get a result in the time domain, multiply the above expression [exp(-gamms)x)] by exp(j(omega)t and take the real part.
I didn't get you. its fine for sinusoidal input . but what will you do for a random white noise input? What is (omega) there? Actually i need the complete time domain output signal for any kind of input? and its not a very good idea to plot frequency resp. by sweeping over the frequency range ! what should be the frequency step? the convenient way is to take PSD of the output of random white noise input so in one go you get the plot of loss from 0 to FS/2 (if fs = 44100 you get it till 22050HZ) which would have taken a lot of time if the program sweeps the frequency with 0.01HZ step all the way down !
thanx any way.
If you have white noise input and want to do rigorous math, the entire approach must be statistical. Of course you can not write down a time-domain output. You have a statistical output. Never-the-less the output due to white noise follows the spectral response of the system so you cannot go wrong by getting a plot of the response.
The time domain output is the cinviolution of the input signal with the impulse response of the system. Since the input is not known you have to leave the output in this integral form. Once you are given a specific input signal then you can do more math in writing the output function. However, if the input is white noise you can never write a specific function in the time domain for the output. The output must be described statistically.
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